Interest help

Question

James contributes $6000 per year into a Traditional IRA earning interest at the rate of 5% per year compounded annually, every year after 35 years of age until his retirement at age 65.

John contributes $5000 per year into a Roth IRA earning interest at the rate of 5% per year compounded annually for a period of 30 years.

The investments of James and John are in a marginal tax bracket of 25% at the time of their retirement. They both wish to withdraw all of the money in their IRAs at retirement.

After all due taxes are paid, who will have the larger amount? By how much will that amount be?

Answer 1

Raven,

 

We need the annuity formula to calculate this.

 

P = PMT[((1+r)ⁿ-1)/r]

PMT = annual contribution

r = annual interest rate

n = number years invested

 

For James we have

P = 6000 [((1+.05)³⁰-1)/.05] = 398,633

At age 65 before any withdrawals, James will have accumulated $398,633

When he withdraws the money, he'll have to pay 25% in taxes, $99,658 and he'll have a meet of $298,975

 

For John we have
P = 5000 [((1+.05)³⁰-1)/.05] = 332,194
At age 65 before any withdrawals, James will have accumulated $332,194

Since John has a Roth IRA, his contributions were already taxed and he owes no tax on the funds he withdraws.

John will net more by

$332194

-298975

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$33,219